Quantum Physics Commons^™

New Exactly Solvable Hamiltonians - Shape Invariance And Self-Similarity, David Barclay, Ranabir Dutt, Asim Gangopadhyaya, Avinash Khare, A. Pagnamenta, Uday Sukhatne

Asim Gangopadhyaya

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission …

Noncentral Potentials And Spherical Harmonics Using Supersymmetry And Shape Invariance, Ranabir Dutt, Asim Gangopadhyaya, Uday Sukhatne

Asim Gangopadhyaya

It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be applied to several problems with noncentral vector and scalar potentials. As examples, we analyze the bound state spectra of an electron in a Coulomb plus an Aharonov – Bohm field and/or in the magnetic field of a Dirac monopole.

Supersymmetric Quantum Mechanics And Solvable Models, Asim Gangopadhyaya, Jonathan Bougie, Jeffrey Mallow, C. Rasinariu

Asim Gangopadhyaya

We review solvable models within the framework of supersymmetric quantum mechanics (SUSYQM). In SUSYQM, the shape invariance condition insures solvability of quantum mechanical problems. We review shape invariance and its connection to a consequent potential algebra. The additive shape invariance condition is specified by a difference-differential equation; we show that this equation is equivalent to an infinite set of partial differential equations. Solving these equations, we show that the known list of h-independent superpotentials is complete. We then describe how these equations could be extended to include superpotentials that do depend on h.

Comment On "Ideal Capacitor Circuits And Energy Conservation" By K. Mita And M. Boufaida [Am. J. Phys. 67 (8), 737-739 (1999)], Asim Gangopadhyaya, Jeffrey Mallow

Asim Gangopadhyaya

No abstract provided.

Renormalization Group Equations In Broken Supersymmetric Theories Using Superspace Methods, Asim Gangopadhyaya, Darwin Chang

Asim Gangopadhyaya

We apply the superfield method with the spurion technique to derive the renormalization-group equations in broken supersymmetric theories. We point out some possible ambiguities in this procedure and show that it is in general necessary to express the supersymmetry-breaking terms in explicit D-type form. We also found that it is possible to construct broken supersymmetric theories where some of the symmetry-breaking parameters do not receive any infinite renormalization.

Coordinate Realizations Of Deformed Lie Algebras With Three Generator, Ranabir Dutt, Asim Gangopadhyaya, C. Rasinariu, Uday Sukhatne

Asim Gangopadhyaya

Differential realizations in coordinate space for deformed Lie algebras with three generators are obtained using bosonic creation and annihilation operators satisfying Heisenberg commutation relations. The unified treatment presented here contains as special cases all previously given coordinate realizations of so(2,1), so(3), and their deformations. Applications to physical problems involving eigenvalue determination in nonrelativistic quantum mechanics are discussed.

Anyonic Superconductivity In A Modified Large-U Hubbard Model, Asim Gangopadhyaya, Prasanta Panigrahi

Asim Gangopadhyaya

A modified large-U Hubbard model at half filling is analyzed by a mean-field approach. Preserving a local U(1) symmetry of the action, the fluctuations about half filling are studied in the spirit of the commensurate-flux-phase condition. The fluctuations then contribute a Chern-Simons term to the tree-level Lagrangian with a coefficient appropriate to that of a half fermion. With the Coulomb repulsion term, we study the low-energy excitations of the model and show the existence of superconductivity in the presence of a four-Fermi interaction term.

Superspace Ward Identities In Supersymmetric Gauge Theories, Asim Gangopadhyaya, Darwin Chang

Asim Gangopadhyaya

In superspace formulation of supersymmetric gauge theories, gauge invariance requires an infinite set of identities between the infinite set of renormalization constants. Using Ward identities in superspace, the same is derived. These identities at one loop level are also demonstrated.

Heterotic Conformal Field Theory And Gepner’S Construction, Darwin Chang, Asim Gangopadhyaya, Alok Kumar, Jin Wang

Asim Gangopadhyaya

We discuss some general properties of heterotic conformal field theory in which conformal anomalies c are different for the left-moving and right-moving sectors. It is precisely this type of theory that can be applied immediately to the construction of heterotic string theory. We discuss a general way of constructing such a theory using free fermions. The construction is then applied to generalize Gepner's construction of superstring solutions using the tensor products of N=2 superconformal field theories.

Variable Renewable Energy In Modeling Climate Change Mitigation Scenarios, Falko Ueckerdt, Robert J. Brecha, Gunnar Luderer, Patrick Sullivan, Eva Schmid, Nico Bauer, Diana Böttger

Robert J. Brecha

This paper addresses the issue of how to account for short‐term temporal variability of renewable energy sources and power demand in long‐term climate change mitigation scenarios in energy‐economic models. An approach that captures in a stylized way the major challenges to the integration of variable renewable energy sources into power systems has been developed. As a first application this approach has been introduced to REMIND‐D, a hybrid energy‐economy model of Germany. An approximation of the residual load duration curve is implemented. The approximating function endogenously changes depending on the penetration and mix of variable renewable power. The approach can thus …

Establishing Building Recommissioning Priorities And Potential Energy Savings From Utility Energy Data, Kevin P. Hallinan, Philip Brodrick, Jessica Northridge, J. Kelly Kissock, Robert J. Brecha

Robert J. Brecha

An energy reduction program for commercial buildings is implemented for a SW Ohio natural gas utility. The aim of this study is to demonstrate that historical utility data for individual building customers, along with knowledge of pertinent building information (square footage, year built, number of floors, height of floors, wall construction type, and use type) available in county auditor databases, could be used to identify the best candidate buildings for recommissioning in terms of energy savings and simple payback. A study is completed for all natural gas customers of a utility in Montgomery and Clinton counties in Ohio. A total …

Cooling Atoms In An Optical Trap By Selective Parametric Excitation, Nicola Poli, Robert J. Brecha, Giacomo Roati, Giovanni Modugno

Robert J. Brecha

We demonstrate the possibility of energy-selective removal of cold atoms from a tight optical trap by means of parametric excitation of the trap vibrational modes. Taking advantage of the anharmonicity of the trap potential, we either selectively remove the most energetic trapped atoms or excite those at the bottom of the trap by tuning the parametric modulation frequency. This process, which had been previously identified as a possible source of heating, also appears to be a robust way for forcing evaporative cooling in anharmonic traps.

Economics Of Nuclear Power And Climate Change Mitigation Policies, Nico Bauer, Robert Brecha, Gunnar Luderer

Robert J. Brecha

The events of March 2011 at the nuclear power complex in Fukushima, Japan, raised questions about the safe operation of nuclear power plants, with early retirement of existing nuclear power plants being debated in the policy arena and considered by regulators. Also, the future of building new nuclear power plants is highly uncertain. Should nuclear power policies become more restrictive, one potential option for climate change mitigation will be less available. However, a systematic analysis of nuclear power policies, including early retirement, has been missing in the climate change mitigation literature. We apply an energy economy model framework to derive …

Two-Level Atom In An Optical Parametric Oscillator: Spectra Of Transmitted And Fluorescent Fields In The Weak Driving Field Limit, James P. Clemens, Perry R. Rice, Pranaw Kumar Rungta, Robert J. Brecha

Robert J. Brecha

We consider the interaction of a two-level atom inside an optical parametric oscillator. In the weak-driving-field limit, we essentially have an atom-cavity system driven by the occasional pair of correlated photons, or weakly squeezed light. We find that we may have holes, or dips, in the spectrum of the fluorescent and transmitted light. This occurs even in the strong-coupling limit when we find holes in the vacuum-Rabi doublet. Also, spectra with a subnatural linewidth may occur. These effects disappear for larger driving fields, unlike the spectral narrowing obtained in resonance fluorescence in a squeezed vacuum; here it is important that …

Renewable Energy In The Context Of Sustainable Development, Jayant Sathaye, Oswaldo Lucon, Atiq Rahman, John Christensen, Fatima Denton, Junichi Fujino, Garvin Heath, Monirul Mirza, Hugh Rudnick, August Schlaepfer, Andrey Shmakin, Gerhard Angerer, Christian Bauer, Morgan Bazilian, Robert J. Brecha, Peter Burgherr, Leon Clarke, Felix Creutzig, James Edmonds, Christian Hagelüken, Gerrit Hansen, Nathan Hultman, Michael Jakob, Susanne Kadner, Manfred Lenzen, Jordan Macknick, Eric Masanet, Yu Nagai, Anne Olhoff, Karen Olsen, Michael Pahle, Ari Rabl, Richard Richels, Joyashree Roy, Tormod Schei, Christoph Von Stechow, Jan Christoph Steckel, Ethan Warner, Tom Wilbanks, Yimin Zhang

Robert J. Brecha

Historically, economic development has been strongly correlated with increasing energy use and growth of greenhouse gas (GHG) emissions. Renewable energy (RE) can help decouple that correlation, contributing to sustainable development (SD). In addition, RE offers the opportunity to improve access to modern energy services for the poorest members of society, which is crucial for the achievement of any single of the eight Millennium Development Goals. Theoretical concepts of SD can provide useful frameworks to assess the interactions between SD and RE. SD addresses concerns about relationships between human society and nature. Traditionally, SD has been framed in the three-pillar model—Economy, …

Ten Reasons To Take Peak Oil Seriously, Robert Brecha

Robert J. Brecha

Forty years ago, the results of modeling, as presented in The Limits to Growth, reinvigorated a discussion about exponentially growing consumption of natural resources, ranging from metals to fossil fuels to atmospheric capacity, and how such consumption could not continue far into the future. Fifteen years earlier, M. King Hubbert had made the projection that petroleum production in the continental United States would likely reach a maximum around 1970, followed by a world production maximum a few decades later. The debate about “peak oil," as it has come to be called, is accompanied by some of the same vociferous denials, …

Video Feature — Banned Books And The Stuart Rose Collection, Robert Brecha, Una Cadegan, John Inglis, Paul Morman

Robert J. Brecha

A faculty panel discussion in two sessions:

Session 1:
The Index: Una Cadegan (history) looks at the current scholarship on the Index of Forbidden Books.
Galileo: Robert Brecha (physics) highlights the banning of Galileo and observational science.

Session 2:
Thomas Aquinas: John Inglis (philosophy) speaks on the banning of Thomas Aquinas's Summa Theologica, the most important book in Catholic intellectual tradition.
Descartes and the Index of Forbidden Books: Paul Morman (history, Distinguished Service Professor) highlights the book by Descartes that he was not allowed to study while a student at UD in the 1960s.

The Sign Learning Kink (Silk) Based Quantum Monte Carlo (Qmc), Xiaoyao Ma, Frank Loffler, Randall W. Hall, Karol Kowalski, Mark Jarrell, Juana Moreno

Randall W. Hall